Human robot interaction is commonly seen in the application of collaborative robots. In order to ensure the safety of the human operator, most existing approaches exploit the idea of compliance control in the design of suitable controllers. In particular, force sensors are often used to estimate the contact force that is essential in the design of the compliance control scheme. However, force sensor-based approaches are not cost-effective. In order to cope with this problem so as to facilitate the implementation of compliance control, this paper aims to compare various observer-based force-sensorless approaches for implementing impedance control of collaborative robot manipulators. Different observer-based approaches, such as the generalized momentum approach, the extended state observer, the modified extended state observer, and the closed-loop disturbance observer are used in this paper to estimate the contact force. Several impedance control experiments conducted on a 6-DOF robot manipulator are used to assess the performances of the aforementioned observer-based approaches. Experimental results indicate that the modified extended state observer exhibits the best performance on contact force estimation among all the tested observer-based approaches.